Here's a tcolorbox version. Just adjust the 2cm
to your liking.

\documentclass{article}
\usepackage[skins]{tcolorbox}
\newtcolorbox{mybox}{enhanced,sharp corners=all,colback=white,colframe=gray,toprule=0pt,bottomrule=0pt,leftrule=1pt,rightrule=1pt,overlay={
\draw[gray,line width=1pt] (frame.north west) -- ++(2cm,0pt);
\draw[gray,line width=1pt] (frame.south east) -- ++(-2cm,0pt);
}}
\usepackage{lipsum}
\begin{document}
\begin{mybox}
\lipsum[2]
\end{mybox}
\end{document}
Update: Title addition. To put more distance between title and text just use bottom=1pt
(or more) in boxed title style
.

\documentclass{article}
\usepackage[skins]{tcolorbox}
\newtcolorbox{mybox}[1]{enhanced,sharp corners=all,colback=white,colframe=gray,toprule=0pt,bottomrule=0pt,leftrule=1pt,rightrule=1pt,overlay={
\draw[gray,line width=1pt] (frame.north west) -- ++(2cm,0pt);
\draw[gray,line width=1pt] (frame.south east) -- ++(-2cm,0pt);
},attach boxed title to top left,boxed title style={frame hidden,interior hidden},title={\color{black}#1}}
\usepackage{lipsum}
\begin{document}
\begin{mybox}{Test}
\lipsum[2]
\end{mybox}
\end{document}
Update 2: If you have a boxed title which is of only one line height you could be interested in this hack:

\documentclass{article}
\usepackage[skins]{tcolorbox}
\newtcolorbox{mybox}[1]{enhanced,sharp corners=all,colback=white,colframe=gray,toprule=0pt,bottomrule=0pt,leftrule=1pt,rightrule=1pt,overlay={
\draw[gray,line width=1pt] (frame.north west) -- ++(2cm,0pt);
\draw[gray,line width=1pt] (frame.south east) -- ++(-2cm,0pt);
},attach boxed title to top left={yshift=-20pt},boxed title style={frame hidden,interior hidden},top=.75cm,title={\bfseries\color{black}#1}}
\usepackage{lipsum}
\begin{document}
\begin{mybox}{Test}
\lipsum[2]
\end{mybox}
\end{document}
Update 3: Here's the "correct" way to change the title height.

\documentclass{article}
\usepackage[skins]{tcolorbox}
\newtcolorbox{mybox}[1]{enhanced,sharp corners=all,colback=white,colframe=gray,toprule=0pt,bottomrule=0pt,leftrule=1pt,rightrule=1pt,overlay={
\draw[gray,line width=1pt] (frame.north west) -- ++(2cm,0pt);
\draw[gray,line width=1pt] (frame.south east) -- ++(-2cm,0pt);
},
coltitle=black,colbacktitle=white,titlerule=0pt,
title={\vskip5pt\bfseries#1}
}
\usepackage{lipsum}
\begin{document}
\begin{mybox}{This is a very long title which seems pretty ridiculous, but is used, although it is nonsense}
\lipsum[2]
\end{mybox}
\end{document}
tcolorbox
. Is that an option? – TeXnician Aug 8 '17 at 17:18